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from sympy.core.numbers import comp, Rational |
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from sympy.physics.optics.utils import (refraction_angle, fresnel_coefficients, |
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deviation, brewster_angle, critical_angle, lens_makers_formula, |
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mirror_formula, lens_formula, hyperfocal_distance, |
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transverse_magnification) |
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from sympy.physics.optics.medium import Medium |
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from sympy.physics.units import e0 |
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from sympy.core.numbers import oo |
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from sympy.core.symbol import symbols |
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from sympy.functions.elementary.miscellaneous import sqrt |
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from sympy.matrices.dense import Matrix |
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from sympy.geometry.point import Point3D |
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from sympy.geometry.line import Ray3D |
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from sympy.geometry.plane import Plane |
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from sympy.testing.pytest import raises |
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ae = lambda a, b, n: comp(a, b, 10**-n) |
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def test_refraction_angle(): |
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n1, n2 = symbols('n1, n2') |
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m1 = Medium('m1') |
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m2 = Medium('m2') |
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r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0)) |
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i = Matrix([1, 1, 1]) |
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n = Matrix([0, 0, 1]) |
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normal_ray = Ray3D(Point3D(0, 0, 0), Point3D(0, 0, 1)) |
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P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1]) |
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assert refraction_angle(r1, 1, 1, n) == Matrix([ |
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[ 1], |
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[ 1], |
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[-1]]) |
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assert refraction_angle([1, 1, 1], 1, 1, n) == Matrix([ |
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[ 1], |
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[ 1], |
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[-1]]) |
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assert refraction_angle((1, 1, 1), 1, 1, n) == Matrix([ |
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[ 1], |
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[ 1], |
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[-1]]) |
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assert refraction_angle(i, 1, 1, [0, 0, 1]) == Matrix([ |
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[ 1], |
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[ 1], |
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[-1]]) |
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assert refraction_angle(i, 1, 1, (0, 0, 1)) == Matrix([ |
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[ 1], |
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[ 1], |
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[-1]]) |
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assert refraction_angle(i, 1, 1, normal_ray) == Matrix([ |
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[ 1], |
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[ 1], |
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[-1]]) |
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assert refraction_angle(i, 1, 1, plane=P) == Matrix([ |
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[ 1], |
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[ 1], |
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[-1]]) |
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assert refraction_angle(r1, 1, 1, plane=P) == \ |
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Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1)) |
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assert refraction_angle(r1, m1, 1.33, plane=P) == \ |
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Ray3D(Point3D(0, 0, 0), Point3D(Rational(100, 133), Rational(100, 133), -789378201649271*sqrt(3)/1000000000000000)) |
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assert refraction_angle(r1, 1, m2, plane=P) == \ |
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Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1)) |
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assert refraction_angle(r1, n1, n2, plane=P) == \ |
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Ray3D(Point3D(0, 0, 0), Point3D(n1/n2, n1/n2, -sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1))) |
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assert refraction_angle(r1, 1.33, 1, plane=P) == 0 |
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assert refraction_angle(r1, 1, 1, normal_ray) == \ |
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Ray3D(Point3D(0, 0, 0), direction_ratio=[1, 1, -1]) |
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assert ae(refraction_angle(0.5, 1, 2), 0.24207, 5) |
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assert ae(refraction_angle(0.5, 2, 1), 1.28293, 5) |
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raises(ValueError, lambda: refraction_angle(r1, m1, m2, normal_ray, P)) |
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raises(TypeError, lambda: refraction_angle(m1, m1, m2)) |
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raises(TypeError, lambda: refraction_angle(r1, m1, m2, None, i)) |
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raises(TypeError, lambda: refraction_angle(r1, m1, m2, m2)) |
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def test_fresnel_coefficients(): |
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assert all(ae(i, j, 5) for i, j in zip( |
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fresnel_coefficients(0.5, 1, 1.33), |
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[0.11163, -0.17138, 0.83581, 0.82862])) |
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assert all(ae(i, j, 5) for i, j in zip( |
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fresnel_coefficients(0.5, 1.33, 1), |
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[-0.07726, 0.20482, 1.22724, 1.20482])) |
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m1 = Medium('m1') |
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m2 = Medium('m2', n=2) |
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assert all(ae(i, j, 5) for i, j in zip( |
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fresnel_coefficients(0.3, m1, m2), |
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[0.31784, -0.34865, 0.65892, 0.65135])) |
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ans = [[-0.23563, -0.97184], [0.81648, -0.57738]] |
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got = fresnel_coefficients(0.6, m2, m1) |
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for i, j in zip(got, ans): |
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for a, b in zip(i.as_real_imag(), j): |
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assert ae(a, b, 5) |
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def test_deviation(): |
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n1, n2 = symbols('n1, n2') |
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r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0)) |
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n = Matrix([0, 0, 1]) |
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i = Matrix([-1, -1, -1]) |
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normal_ray = Ray3D(Point3D(0, 0, 0), Point3D(0, 0, 1)) |
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P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1]) |
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assert deviation(r1, 1, 1, normal=n) == 0 |
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assert deviation(r1, 1, 1, plane=P) == 0 |
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assert deviation(r1, 1, 1.1, plane=P).evalf(3) + 0.119 < 1e-3 |
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assert deviation(i, 1, 1.1, normal=normal_ray).evalf(3) + 0.119 < 1e-3 |
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assert deviation(r1, 1.33, 1, plane=P) is None |
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assert deviation(r1, 1, 1, normal=[0, 0, 1]) == 0 |
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assert deviation([-1, -1, -1], 1, 1, normal=[0, 0, 1]) == 0 |
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assert ae(deviation(0.5, 1, 2), -0.25793, 5) |
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assert ae(deviation(0.5, 2, 1), 0.78293, 5) |
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def test_brewster_angle(): |
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m1 = Medium('m1', n=1) |
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m2 = Medium('m2', n=1.33) |
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assert ae(brewster_angle(m1, m2), 0.93, 2) |
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m1 = Medium('m1', permittivity=e0, n=1) |
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m2 = Medium('m2', permittivity=e0, n=1.33) |
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assert ae(brewster_angle(m1, m2), 0.93, 2) |
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assert ae(brewster_angle(1, 1.33), 0.93, 2) |
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def test_critical_angle(): |
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m1 = Medium('m1', n=1) |
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m2 = Medium('m2', n=1.33) |
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assert ae(critical_angle(m2, m1), 0.85, 2) |
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def test_lens_makers_formula(): |
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n1, n2 = symbols('n1, n2') |
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m1 = Medium('m1', permittivity=e0, n=1) |
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m2 = Medium('m2', permittivity=e0, n=1.33) |
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assert lens_makers_formula(n1, n2, 10, -10) == 5.0*n2/(n1 - n2) |
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assert ae(lens_makers_formula(m1, m2, 10, -10), -20.15, 2) |
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assert ae(lens_makers_formula(1.33, 1, 10, -10), 15.15, 2) |
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def test_mirror_formula(): |
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u, v, f = symbols('u, v, f') |
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assert mirror_formula(focal_length=f, u=u) == f*u/(-f + u) |
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assert mirror_formula(focal_length=f, v=v) == f*v/(-f + v) |
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assert mirror_formula(u=u, v=v) == u*v/(u + v) |
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assert mirror_formula(u=oo, v=v) == v |
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assert mirror_formula(u=oo, v=oo) is oo |
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assert mirror_formula(focal_length=oo, u=u) == -u |
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assert mirror_formula(u=u, v=oo) == u |
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assert mirror_formula(focal_length=oo, v=oo) is oo |
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assert mirror_formula(focal_length=f, v=oo) == f |
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assert mirror_formula(focal_length=oo, v=v) == -v |
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assert mirror_formula(focal_length=oo, u=oo) is oo |
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assert mirror_formula(focal_length=f, u=oo) == f |
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assert mirror_formula(focal_length=oo, u=u) == -u |
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raises(ValueError, lambda: mirror_formula(focal_length=f, u=u, v=v)) |
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def test_lens_formula(): |
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u, v, f = symbols('u, v, f') |
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assert lens_formula(focal_length=f, u=u) == f*u/(f + u) |
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assert lens_formula(focal_length=f, v=v) == f*v/(f - v) |
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assert lens_formula(u=u, v=v) == u*v/(u - v) |
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assert lens_formula(u=oo, v=v) == v |
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assert lens_formula(u=oo, v=oo) is oo |
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assert lens_formula(focal_length=oo, u=u) == u |
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assert lens_formula(u=u, v=oo) == -u |
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assert lens_formula(focal_length=oo, v=oo) is -oo |
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assert lens_formula(focal_length=oo, v=v) == v |
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assert lens_formula(focal_length=f, v=oo) == -f |
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assert lens_formula(focal_length=oo, u=oo) is oo |
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assert lens_formula(focal_length=oo, u=u) == u |
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assert lens_formula(focal_length=f, u=oo) == f |
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raises(ValueError, lambda: lens_formula(focal_length=f, u=u, v=v)) |
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def test_hyperfocal_distance(): |
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f, N, c = symbols('f, N, c') |
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assert hyperfocal_distance(f=f, N=N, c=c) == f**2/(N*c) |
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assert ae(hyperfocal_distance(f=0.5, N=8, c=0.0033), 9.47, 2) |
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def test_transverse_magnification(): |
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si, so = symbols('si, so') |
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assert transverse_magnification(si, so) == -si/so |
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assert transverse_magnification(30, 15) == -2 |
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def test_lens_makers_formula_thick_lens(): |
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n1, n2 = symbols('n1, n2') |
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m1 = Medium('m1', permittivity=e0, n=1) |
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m2 = Medium('m2', permittivity=e0, n=1.33) |
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assert ae(lens_makers_formula(m1, m2, 10, -10, d=1), -19.82, 2) |
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assert lens_makers_formula(n1, n2, 1, -1, d=0.1) == n2/((2.0 - (0.1*n1 - 0.1*n2)/n1)*(n1 - n2)) |
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def test_lens_makers_formula_plano_lens(): |
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n1, n2 = symbols('n1, n2') |
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m1 = Medium('m1', permittivity=e0, n=1) |
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m2 = Medium('m2', permittivity=e0, n=1.33) |
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assert ae(lens_makers_formula(m1, m2, 10, oo), -40.30, 2) |
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assert lens_makers_formula(n1, n2, 10, oo) == 10.0*n2/(n1 - n2) |
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